Study on Anisotropic Plastic Deformation of Mg-Alloys using
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Study on Anisotropic Plastic Deformation of Mg-Alloys using Crystal Plasticity p * F F F ⋅ = Motivation Motivation Deformation Mechanisms of Magnesium Hexagonal Closed Packed Crystal Crystal Plasticity Model Crystal Plasticity Model Validation of Model Parameters Validation of Model Parameters M. Homayonifar, S. Graff, D. Steglich, W. Brocks Institute of Materials Research, GKSS Research Centre, Max-Planck-Str. 1, 21502 Geesthacht Finite Element Model for Deep Drawing Process of Magnesium Sheets. Crystal Plasticity for Process Simulation ( ) [ ] ) *( * * * * ) *( ) : ( α α α τ m D T T D D I T T n ⋅ ⋅ + ⋅ − + ⋅ = ∇ & ∑ = ⋅ − α α α α γ ) ( ) ( ) ( 1 n m F F p p & & ( ) ( ) ( ) ( ) ( ) ( ) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = α α α α α α τ τ τ τ γ γ Y n Y sign 0 & & Deformation gradient: Rate of the RSS: Schmid’s law: Rate-dependent viscoplasticity: ( ) ( ) α α ρ ρ τ * * . . m T n o = ( ) ( ) ( ) α αβ α γ γ τ & & ∑ = h Y ( ) dt t o ∑∫ = α α γ γ & ( ) o h h = γ () ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = ∞ ∞ τ γ τ τ γ o o o h h h exp 1 () ⎪ ⎩ ⎪ ⎨ ⎧ > ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ≤ = − ref m ref o ref o h h h γ γ γ γ γ γ γ 1 Voce-hardening: Linear-power law hardening: Linear hardening: ( ) ( ) ( ) parameters 38 Total of values sixteen , , , , of sets four , of set one 0 = ∞ αβ τ τ γ γ h h m n o ref o & Plastic Potential for Process Simulation Plastic Potential for Process Simulation Setup of Channel Die Test RVE for Mg Single Crystal RVEs for Textured Mg Polycrystal Finite Element Model for Channel Die Test Comparison with experimental results (Kelley & Hosford,1968) validates the sets of the identified parameters for single and polycrstals: Experiment Simulation Texture Analysis of ZM21 Mg Alloys (WZW, GKSS, 2007) Discretising of Materials Texture to Implement in Finite Element Models Discretising Finite Element Model of Biaxial Test for Proportional Loading Paths Isostrain Curves for Different Magnesium Alloy Textures Random Texture (cast product) Rolled Plate Texture Biaxial Test Phenomenological Model Deep Drawing Process Contact: M. Homayonifar, Tel: +494152-872605, E-mail: [email protected], Internet: http://www.gkss.de/ Identification with help of Channel Die Test: Crystal Plasticity model introduces 38 parameters. Despite its attractive specific strength, applications of Magnesium alloys have been restricted to cast or simply formed products. For production of complex shaped parts, e.g. in automotive and aerospace industries, a prediction of forming capacities with help of finite element method is required. For a fast and efficient simulation, the anisotropic mechanical behavior of Magnesium has to be described by a phenomenological plastic potential. Crystal plasticity helps to identify its parameters.
Transcript of Study on Anisotropic Plastic Deformation of Mg-Alloys using
Study on Anisotropic Plastic Deformationof Mg-Alloys using Crystal Plasticity
p* FFF ⋅=
MotivationMotivation
Deformation Mechanisms of Magnesium Hexagonal Closed Packed Crystal
Crystal Plasticity ModelCrystal Plasticity Model
Validation of Model ParametersValidation of Model Parameters
M. Homayonifar, S. Graff, D. Steglich, W. Brocks
Institute of Materials Research, GKSS Research Centre, Max-Planck-Str. 1, 21502 Geesthacht
Finite Element Model forDeep Drawing Process of Magnesium Sheets.
Crystal Plasticity for Process Simulation
( ) [ ] )*(****)*( ):( ααατ mDTTDDITTn ⋅⋅+⋅−+⋅= ∇&
∑=⋅ −
α
αααγ )()()(1 nmFF pp && ( )
( )
( )
( )
( )
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛= α
α
α
α
α
α
ττ
ττ
γγ
Y
n
Y
sign0&
&
Deformation gradient:
Rate of the RSS:
Schmid’s law:
Rate-dependent viscoplasticity:
( ) ( )αα
ρρτ ** .. mTno
= ( ) ( ) ( )α
αβ
α γγτ && ∑= hY
( ) dtt
o∑ ∫=α
αγγ &
( )ohh =γ
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
∞∞τγ
ττγ oo
o
hhh exp1
( )⎪⎩
⎪⎨
⎧
>⎟⎟⎠
⎞⎜⎜⎝
⎛≤
=−
ref
m
ref
o
refo
h
hh
γγγγ
γγγ
1
Voce-hardening:
Linear-power law
hardening:
Linear hardening:
( )( )
( )parameters38Total
ofvaluessixteen,,,,ofsetsfour
,ofsetone
0
=
∞
αβ
ττγγ
hhmn
oref
o&
Plastic Potential for Process SimulationPlastic Potential for Process Simulation
Setup of Channel Die Test RVE for Mg Single Crystal
RVEs for Textured Mg PolycrystalFinite Element Model for
Channel Die Test
Comparison with experimental results (Kelley & Hosford,1968)validates the sets of the identified parameters for single and polycrstals:
Experiment SimulationTexture Analysis of ZM21
Mg Alloys (WZW, GKSS, 2007)Discretising of Materials Texture to Implement in Finite Element Models
Discretising
Finite Element Model of Biaxial Test for Proportional Loading Paths
Isostrain Curves for Different Magnesium Alloy Textures
Random Texture (cast product) Rolled Plate Texture
Biaxial Test Phenomenological Model Deep Drawing Process
Contact: M. Homayonifar, Tel: +494152-872605, E-mail: [email protected], Internet: http://www.gkss.de/
Identification with help of Channel Die Test:
Crystal Plasticity model introduces 38 parameters.
Despite its attractive specific strength, applications of Magnesium alloys have been restricted to cast or simply formed products. For production of complex shaped parts, e.g. in automotive and aerospace industries, a prediction of forming capacities with help of finite element method is required. For a fast and efficient simulation, the anisotropic mechanical behavior of Magnesium has to be described by a phenomenological plastic potential. Crystal plasticity helps to identify its parameters.
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